Fe-vacancy order and superconductivity intetragonal β-Fe1-xSeTa-Kun Chena,1, Chung-Chieh Changa, Hsian-Hong Changb, Ai-Hua Fanga, Chih-Han Wanga, Wei-Hsiang Chaoa,Chuan-Ming Tsenga, Yung-Chi Leea,c, Yu-Ruei Wua, Min-Hsueh Wena, Hsin-Yu Tangd,e, Fu-Rong Chena,d,Ming-Jye Wanga,b, Maw-Kuen Wua,c,f,1, and Dirk Van Dycke

aInstitute of Physics, Academia Sinica, Taipei 115, Taiwan; bInstitute of Astronomy and Astrophysics, Academia Sinica, Taipei 106, Taiwan; Departments ofcPhysics and dEngineering and System Science, National Tsing Hua University, Hsinchu 300, Taiwan; eElectron Microscopy for Materials Science, Departmentof Physics, University of Antwerp, 2020 Antwerp, Belgium; and fDepartment of Physics, National Dong Hwa University, Hualien 974, Taiwan

Contributed by Maw-Kuen Wu, November 21, 2013 (sent for review October 17, 2013)

Several superconducting transition temperatures in the range of30–46 K were reported in the recently discovered intercalated FeSesystem (A1-xFe2-ySe2, A = K, Rb, Cs, Tl). Although the superconduct-ing phases were not yet conclusively decided, more than one mag-netic phase with particular orders of iron vacancy and/or potassiumvacancy were identified, and some were argued to be the parentphase. Here we show the discovery of the presence and orderingof iron vacancy in nonintercalated FeSe (PbO-type tetragonalβ-Fe1-xSe). Three types of iron-vacancy order were found throughanalytical electron microscopy, and one was identified to be non-superconducting and magnetic at low temperature. This discoverysuggests that the rich-phases found in A1-xFe2-ySe2 are not exclu-sive in Fe-Se and related superconductors. In addition, the mag-netic β-Fe1-xSe phases with particular iron-vacancy orders are morelikely to be the parent phase of the FeSe superconducting systeminstead of the previously assigned β-Fe1+δTe.

magnetism | phase diagram

The iron pnictide superconductors have opened the door toa new way to obtain superconductivity at very high temper-

atures. β-Fe1+δSe is remarkable among those superconductors inthat it contains the essential electronic and structural con-stituents required for superconductivity without the conceptualcomplexity seen in other systems (1). Previous studies showedthat the superconducting property of β-Fe1+δSe made underhigh-temperature thermodynamic conditions is very sensitive tostoichiometry (1, 2). In the Fe-Se binary phase diagram (2–4),the PbO-type tetragonal structure (the β phase) only stabilized atthe Fe-rich side (δ = 0.01–0.04), whereas bulk superconductivitywas observed in samples with δ close to 0.01 (5). McQueen et al.showed no superconductivity for samples with δ = 0.03 (5). Onthe other hand, the fact that only one superconducting phase hasbeen reported in FeSe, unlike the other Fe-As–based super-conductors that exhibit clear doping dependence of supercon-ductivity and the absence of superconductivity in FeTe, led to thesuggestion that FeTe is the nonsuperconducting parent com-pound of FeSe (6). Thus, the phase diagram derived from thispicture shows very different features compared with other Fe-As–based superconductors (6, 7). In this work, we use low-temperaturesynthesis methods to prepare β-Fe1-xSe for a wide range ofcompositions, which allows for the determination for thecomposition-dependent electronic behavior for this importantsuperconducting system.The recent discovered alkali/alkaline-intercalated iron sele-

nide (A1-xFe2-ySe2) superconductors with rich superconductingphases, where A = K, Rb, Cs, Tl, attracted great attention notonly due to its high superconducting transition temperature (Tc,up to 46 K) (8), but also because of their dissimilar character-istics compared with other iron-based superconductors, especiallyits seemingly intrinsic multiphase nature and the presence of ironvacancies and orders in the nonsuperconducting regime (9–13).The most frequently observed Fe-vacancy order in A1-xFe2-ySe2 is

theffiffiffi

5p

×ffiffiffi

5p

× 1 superstructure, which yields a phase of A0.8Fe1.6Se2(or A2Fe4Se5). Scanning tunneling microscopy (STM) (11, 14,15) and transport studies (12, 13, 16, 17) showed that A2Fe4Se5 isan antiferromagnetic (AFM) insulator. Neutron scattering mea-surements (9) revealed a blocked checkerboard AFM with mag-netic moments along the c axis for A2Fe4Se5, ordered at atemperature as high as >500 K, with an unexpected large or-dered magnetic moment of ∼3.3 μB/Fe at 10 K. Experimentshave further shown that the type of vacancy and magnetic ordersis highly sensitive to the stoichiometry (x and y) of A1-xFe2-ySe2.Reports have shown the existence of other Fe-vacancy order withthe forms

ffiffiffi

2p

×ffiffiffi

2p

× 1 (10),ffiffiffi

2p

× 2ffiffiffi

2p

× 1 (13, 18), andffiffiffi

8p

×ffiffiffiffiffi

10p

× 1 (19). However, the magnetic properties such as the typeand transition temperature of the magnetic order are far lessstudied compared with that of the K2Fe4Se5 phase. In addi-tion, there were also results showing in K1-xFe2-ySe2 samples witha typical Tc = 31 K and additional superconducting phase withTc = 44 K (20), whereas no clear identification of the new phaseswas available.The complexity of phases and phase separation during crystal

preparation in A1-xFe2-ySe2 make it difficult to conclusively verifythe phase-property relationship, even for the superconductingphases. β-Fe1+δSe, on the other hand, has the simplest structureamong all iron-based superconductor families. Several surprisingresults related to the Fe-Se system appeared in the literatureduring the last few years, including the enhancement of Tc to about40 K under high pressure (21–23) and the intriguing extremely highTc (with a superconducting energy gap of ∼20 meV) in molecular

Significance

We report the observation in the FeSe system of variousFe-vacancy orders, which are similar to those discovered inA1-xFe2-ySe2 superconductors. We observed at least three dif-ferent Fe-vacancy orders, and one was identified to be non-superconducting and magnetic at low temperature, whichimplies a rich-phases nature of Fe-based superconductors. Con-sequently, we propose the existence of a modified phase dia-gram for the Fe-Se superconducting system. This discoveryprovides new opportunities to investigate the correlation be-tween superconductivity and the Fe-vacancy order, whichis critical to understand the origin of superconductivity ofFeSe and related superconductors.

Author contributions: M.-K.W. designed research; T.-K.C., C.-C.C., H.-H.C., A.-H.F., C.-H.W.,W.-H.C., C.-M.T., Y.-C.L., Y.-R.W., and M.-H.W. performed research; T.-K.C., C.-C.C., H.-H.C.,A.-H.F., C.-M.T., H.-Y.T., F.-R.C., M.-J.W., and D.V.D. analyzed data; and T.-K.C. andM.-K.W. wrote the paper.

The authors declare no conflict of interest.

Data deposition: Crystal structure parameters are provided in Table S4.1To whom correspondence may be addressed. E-mail: tkchen@phys.sinica.edu.tw ormkwu@mail.ndhu.edu.tw.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1321160111/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1321160111 PNAS | January 7, 2014 | vol. 111 | no. 1 | 63–68

PHYS

ICS

beam epitaxy (MBE)-grown single-layer FeSe (24–26). We alsodemonstrated the presence of a superconducting-like featurewith Tc close to 40 K in samples of nano-dimensional form (27).Therefore, it is quite natural to ask whether the presence of thecomplex phases observed in A1-xFe2-ySe2 compounds and Fe-vacancy order exist in samples without alkaline metals. Here wepresent the first discovery of iron vacancies and three types ofvacancy orders in tetragonal β-Fe1-xSe, characterized by analyt-ical transmission electron microscopy (TEM). Our observationsimply that an unprecedented phase diagram should be consideredin the Fe-Se superconductors.

Results and DiscussionFig. 1A is the TEM image of a FeSe nanowire, which exhibits thetetragonal symmetry identified from selected area electron dif-fraction (SAED) shown in Fig. 1B. In contrast to the expectation,electrical resistivity measurements on these nanowires showedthat they were not superconducting, as displayed in the inset ofFig. 1A. To understand the reason for not observing supercon-ductivity, we performed a more detailed electron diffraction of

the nanowires. Fig. 1B shows the SAED pattern taken froma tetragonal FeSe nanowire, with clear superstructure spots onthe reciprocal a*-b* plane that could be unambiguously identi-fied as the

ffiffiffi

5p

×ffiffiffi

5p

× 1 Fe-vacancy order by the unique super-structure wave vector q1 = (1/5, 3/5, 0). This order is exactly thesame as the one found in A2Fe4Se5. We then denominated thisphase as β-Fe4Se5 (x = 0.2). This observation resolved our puzzleof the absence of superconductivity in these FeSe nanowires. Asubsequent question was whether this Fe-vacancy order exists inother FeSe materials? We decided to examine the other FeSesamples we synthesized, including particles and sheets preparedusing hydrothermal process (27), crystals grown at high pressure(28), and samples from K2Fe4Se5 crystals after extracting K byiodine (Materials and Methods). It is noted that most of thesesamples are in nano-dimensional forms, either as a nanoparticle(0-dimension), nanowire (1-dimension), or nanosheet (2-dimension).Fig. 2A shows a typical SAED pattern of a sample from the Kextraction of a K2Fe4Se5 crystal, with superstructure spots

ffiffiffi

5p

×ffiffiffi

5p

× 1. The frequently observed twinned superstructure inA2Fe4Se5 was also found in these samples and nanosheets fromthe hydrothermal process, as shown in Fig. 2 B and C. The dif-ference between the SAED patterns in Fig. 2 B and C is thesystematic absence in (h00), (0k0), h odd, k odd, shown by a bluearrow. The appearance of this systematic absence has been at-tributed to three possibilities: (i) potassium vacancy orders (12,13), (ii) phase transformation due to sample oxidation (29), and(iii) Fe-Fe paring (dimer formation) (5). The former two are lesspossible in our case because no potassium is in the sample, andthe last one was known to appear at a very low temperature, i.e.,11 K. An alternative explanation for the appearance of theseforbidden spots will be given when Fe-vacancy order in β-Fe3Se4is introduced.Fig. 2E shows the temperature dependence of the magnetic

susceptibility of a collection of β-Fe4Se5 nanosheets. The zero-field-cooled (ZFC) curve reveals a broad transition around 100K, consistent with the resistivity data from a β-Fe4Se5 sheet (Fig.3F), where at low temperatures (2–45 K), the data can be best fitwith a metal-insulator transition following the 3D Mott variablerange hopping model. It is interesting to note that the suscepti-bility of the β-Fe4Se5 sheets from the K2Fe4Se5 crystal show strong

Fig. 1. (A) TEM image of a FeSe nanowire. (Inset) Temperature-dependenttransport property of the same nanowire. (B) The SAED pattern of thenanowire, revealing a tetragonal lattice along the [001] zone-axis direction.Superstructure wave vectors q1 = (1/5, 3/5, 0) and q2 = (3/5, 1/5, 0) are in-dicated by red arrows.

Fig. 2. Experimental SAED patterns of (A) untwinned and (B and C) twinned β-Fe4Se5. Superstructure wave vectors q1 = (1/5, 3/5, 0) and q2 = (3/5, 1/5, 0) areindicated by red arrows. The blue arrow in C points out one of the systematic absence in (h00), (0k0), h odd, k odd, which is not visible in B. (D) Schematicdrawing of atom arrangements for untwinned and twinned β-Fe4Se5. (E) Temperature-dependent susceptibility of a collection of β-Fe4Se5 nanosheets. (LeftInset) Curie-Weiss fit in the high temperature range 200 K < T < 300 K: χ =C=T − θ

+ χ′, where C is the Curie constant, θ is the Curie temperature, and χ′ is thetemperature-independent susceptibility. (Right Inset) Temperature-dependent susceptibility of the same β-Fe4Se5 nanosheets after annealed at 700 °C invacuum and quenched to room temperature. (F) Resistance as a function of temperature for three β-Fe4Se5 sheets, cleaved by scotch-tape from differentpieces in the same batch. Current was applied within the a-b plane. (Inset) Natural logarithmic resistance plotted against 1/T1/4, in which the data between2 and 45 K are fit by the 3D Mott variable range hopping model: R∼ exp½−ðT*=TÞ1=4�, where T* is the characteristic temperature. (G) Temperature-dependentsusceptibility of a β-Fe4Se5 sheet. Magnetic field was applied along and perpendicular to the sheet normal, i.e., the c axis of the tetragonal lattice.

64 | www.pnas.org/cgi/doi/10.1073/pnas.1321160111 Chen et al.

orientation dependence, as shown in Fig. 3G. Our observationsclearly indicated that β-Fe4Se5 is an antiferromagnetic insulator atlow temperatures, similar to that of the K2Fe4Se5 (12, 17). Theestimated magnetic moment from the susceptibility data (left insetof Fig. 2E) above 200 K is about 0.003 μB using the Curie-Weissfit. A detailed magnetic structure of the β-Fe4Se5 sample is cur-rently under investigation using neutron scattering. We furtherfound that by annealing the β-Fe4Se5 nanosheets at 700 °C in vac-uum and quenching to room temperature, it became supercon-ducting with a Tc onset of 8.5 K (right inset of Fig. 2E), similar tothat of the β-Fe1+δSe.More surprises arose when we looked into details of additional

synthesized samples. Besides theffiffiffi

5p

×ffiffiffi

5p

× 1 Fe-vacancy order,we observed several different types of Fe-vacancy order in te-tragonal β-Fe1-xSe. The second type of Fe-vacancy order weobserved is shown in Fig. 3. We recorded five zone-axis patterns(four were shown in Fig. 3 and the other one in Fig. S1) with 12measured interplanar spacings (Table S1) and four angles be-tween zone-axis patterns (Table S2). They are very close to thosefrom superconducting tetragonal β-Fe1+δSe, yet not exactly thesame. The tilting procedure during SAED patterns acquirement(shown in Fig. S2A) and the angles between zone-axis patternssummarized in Table S3 also indicate that it is closer to a te-tragonal phase than other phases in the Fe-Se phase diagram (3).We refined the lattice parameters using a tetragonal lattice yieldinga = 3.67(1) Å and c = 5.70(3) Å, about 3% shrinkage along thea and b axes and 3% elongation along the c axis, compared with the(bulk) tetragonal β-Fe1+δSe (a = 3.775 Å and c = 5.527 Å) (3).

However, we could not assign the presence of extra rows of spot inthe [−121] zone-axis pattern (Fig. 4B, indicated by white arrows) toany of the indexes or double diffractions in tetragonal β-Fe1+δSe.In fact, these superlattice spots are too strong, making them lesslikely to be the result of either symmetry breaking by atomicdisplacements in FeSe (5) or charge density wave (CDW) (30) atlow temperatures. We thus considered the modulation of atomssuch as interstitials and vacancies of Fe and Se. Detailed struc-ture calculations and simulations allowed us to exclude the or-dering of Fe interstitials and Se vacancies (see SI Text for details).Our calculation suggested a superstructure of

ffiffiffi

2p

×ffiffiffi

2p

witha d100 shift every other (001) plane (the FeSe4 tetrahedronlayer), as illustrated in Fig. 3C. This superstructure generateddiffraction patterns that are in excellent agreement with thoseexperimental SAED patterns. This phase was denominated asβ-Fe3Se4 (x = 0.2), and we found this phase in two differentsamples prepared by a high pressure route (Fig. 3) and a hy-drothermal chemical route (Fig. S3). However, it is noted thatthe β-Fe3Se4 phase in Fig. 3 is not a unique solution for theseSAED patterns. For example, the superstructure in Fig. 5E thatshows a 1 × 2 order could as well generate the same SAED pat-terns, with doubled modulation along the <111> direction. Be-cause the particle investigated in this study was along the [−121]direction when the sample holder was inserted, it was not possibleto tilt to the c axis where the aforementioned two types of ordercould be easily distinguished. Another feature to note is that thec axis zone pattern of β-Fe3Se4 is similar to that of the super-conducting β-Fe1+δSe, except that the systematic absences in

Fig. 3. From Left to Right: experimental SAED and simulated kinematical electron diffraction (KED) patterns of β-Fe3Se4 and β-FeSe in the zone axes of (A)[−121] and (B) [−111]. Other zone-axis patterns are shown in Fig. S1. White arrows in A indicate extra rows of spots compared with the KED pattern of β-FeSe.Superstructure wave vector q3 = (1/2, 1/2, 1/2) is indicated by a red arrow. Crosses in the KED patterns of β-FeSe denote double diffraction spots. (C) Schematicdrawings of atom arrangements for β-Fe3Se4 from different viewing directions. Solid lines enclose the I-cell for Fe vacancies.

Chen et al. PNAS | January 7, 2014 | vol. 111 | no. 1 | 65

PHYS

ICS

(h00), (0k0), h odd, k odd, are now visible (Fig. S4). It is thuspossible that the SAED patterns obtained in Fig. 1 B and C arewithout and with β-Fe3Se4 as a second phase in the field ofstudy, respectively. It was reported that the

ffiffiffi

2p

×ffiffiffi

2p

(× 1) squareFe-vacancy order (Fig. 5C) was shown theoretically to not beenergetically favorable compared with the rhombus order (

ffiffiffi

2p

×2

ffiffiffi

2p

; Fig. 5D) (31). In fact, without considering the magneticmoments of Fe (nonmagnetic state), the square orderedstructure has lower energy than the rhombus ordered pattern(31), although the rhombus order would become a more favor-able state with an A-collinear AFM order (31). A more detailedtheoretical study will clarify if the in-plane square order witha d100 shift every other plane with AFM orders would becomemore favorable.The third type of Fe-vacancy order is illustrated in Fig. 4

(crystal structure parameters of the three observed phases aresummarized in Table S4). Five zone-axis patterns (four areshown in Fig. 4 and the other in Fig. S5) were recorded, and thefundamental Bragg spots yielded a tetragonal lattice with a =3.76(1) Å and c = 5.47(3) Å, about 1% shrinkage along the c axis,compared with the tetragonal β-Fe1+δSe (a = 3.775 Å and c =5.527 Å) (3). Although we could not record the c axis zonepattern due to the limitation of the double tilt holder, we can stillresolve the superstructure by the unique modulation wave vec-tors q4 = (2/5, 1/5, 0) and q5 = (1/5, 2/5, 0), as shown in Fig. 4 Band D, respectively. A twinned Fe-vacancy order of

ffiffiffiffiffi

10p

×ffiffiffiffiffi

10p

with a 1/2d310 shift every other (001) plane yielding an I-cell forvacancies is realized as illustrated in Fig. 4 and is thus assigned asβ-Fe9Se10 (x = 0.1). This superstructure has not been observed inA1-xFe2-ySe2, although it is not necessary to be unique in β-Fe1-xSe.

Fig. 5 shows a number of Fe-vacancy orders possibly observedin β-Fe1-xSe, from x = 0.5 to x = 0.1, with the vacancies distributedas uniformly as possible in the iron plane. We believe that undersuitable conditions, other vacancy orders could possibly exist aswell. It is surprising to see that, through unconventional routes,a PbO-type tetragonal β-Fe1-xSe compound exists in a composi-tion range far beyond the previous reported range (2–4) toa region with a great deficiency of iron (maximum x = 0.25 thusfar). Thus, we need to modify the Fe-Se binary phase diagram.Moreover, our finding not only reflects the fact that the previousarguments on the superconductivity in the Fe-Se system may beincomplete but also provides an alternative route to dope or totune the Fe-based superconductors. In fact, when examining inmore detail previous literature, we found that in MBE-grownultrathin FeSe films, the superconductivity could be completelydestroyed by Se doping (32). The films were semiconducting wherethe extra Se dopants were ordered into a

ffiffiffi

5p

×ffiffiffi

5p

superstructureat a high doping concentration (figure S5 in ref. 32). Such anobservation is consistent with the presence of Fe vacancies in a Se-rich growth environment and ordering into superstructures inthese ultrathin FeSe films.Based on the observation in this study, we proposed a tem-

perature-doping phase diagram for the Fe-Se superconductingsystem, as illustrated in Fig. 6, which is very similar to the phasediagram of the superconducting La2CuO4+y (33). The magneticand insulating/semiconducting phases of β-Fe1-xSe with Fe-vacancyorders may act as the parent phase of FeSe superconductor, in-stead of the previously argued β-Fe1+δTe (6), which shows dif-ferent magnetic and electronic features compared with β-Fe1+δSe(25, 34–36). The superconducting β-Fe1.01Se with Tc = 8.5 K could

Fig. 4. (Left) Experimental SAED and (Middle) simulated KED patterns of twinned β-Fe9Se10 in the zone axes of (A) [−212] and (B) [−121]. Other zone-axispatterns are shown in Fig. S5. Superstructure wave vectors q4 = (1/5, 2/5, 0) and q5 = (2/5, 1/5, 0) are indicated by blue arrows. The twinned supersturcturalreflections are illustrated by blue and red circles. (C ) Schematic drawing of atom arrangements for twinned and untwinned β-Fe9Se10. Solid lines enclosethe I-cell for Fe vacancies.

66 | www.pnas.org/cgi/doi/10.1073/pnas.1321160111 Chen et al.

in fact be in the overdoped regime in our proposed phase diagram,because we showed that it could result from the β-Fe4Se5 nano-sheets by annealing at 700 °C in a vacuum and then quenching toroom temperature. Further introduction of Fe suppresses both thetetragonal-to-orthorhombic structural transition and supercon-ductivity as suggested byMcQueen et al. (5). β-Fe1-xSe with vacancyorders could exhibit particular AFM orders at a low temperatureand are not superconducting. Doping or suppression of AFMorders may initiate superconductivity. In fact, recent experimental(37, 38) and theoretical (39) evidence suggested that disorder ofFe vacancies or suppression of the Fe-vacancy orders may bring thereemergence of superconductivity in K1-xFe2-ySe2. Efforts to examinethe correlation between the suppression of Fe-vacancy orders andsuperconductivity in β-Fe1-xSe are currently in progress.

In summary, we report the discovery of the presence and or-dering of iron vacancies in PbO-type tetragonal β-Fe1-xSe. An-alytical TEM indicates that at least three types of Fe-vacancy orderswere found:

ffiffiffi

2p

×ffiffiffi

2p

with a d100 shift every other (001) plane,namely β-Fe3Se4 (x = 0.25);

ffiffiffi

5p

×ffiffiffi

5p

× 1, namely β-Fe4Se5 (x =0.2); and

ffiffiffiffiffi

10p

×ffiffiffiffiffi

10p

with a 1/2d310 shift every other (001) plane,namely β-Fe9Se10 (x = 0.1), similar to the recently discovered Fe-vacancy orders in A1-xFe2-ySe2 (A = K, Rb, Cs, Tl). No super-conductivity was observed in β-Fe4Se5. Instead, a broad magnetictransition was found around 100 K. This discovery suggests thatthe rich-phases found in A1-xFe2-ySe2 may not be exclusive casesin iron-based superconductors. Furthermore, the magnetic andsemiconducting/insulating β-Fe4Se5 or other β-Fe1-xSe phaseswith a particular Fe-vacancy order may serve as the parent phaseof the Fe-Se superconducting system instead of the previouslyassigned β-Fe1+δTe. Our finding creates interest for future tests,both experimentally and theoretically, of the role of Fe vacanciesor dopants in iron-based superconductors.

Materials and MethodsCrystals. FeSe crystals were synthesized via a high-pressure route: Fe and Sepowders (3-N purity) with an appropriate ratio [1.03:1 in atomic percentage(at%)] weremixed and cold pressed into pellets. The pellet was placed in a BNcrucible mounted inside a pyrophyllite cube with a graphite heater, as-sembled in a wedge-type cubic-anvil high-pressure apparatus (model TRYCA350; SANKYO Co. Ltd.). A pressure of ∼2.8 GPa was applied at room tem-perature and throughout the whole process. The temperature was rampedup to 1,050 °C and held for 1.25 h to form the melt. Then it was cooledwithin 30 minutes to 850 °C and quenched to 350 °C for in situ annealing.After a 30-minute annealing, it was quenched to room temperature.

Crystal-Like Sheets. For small c axis–oriented β-Fe4Se5 sheets, KxFe1.6+ySe2crystals were first made using the Bridgman method with a starting com-position of K0.8Fe2Se2 (40). Potassium in these c axis–oriented pieces ofKxFe1.6+ySe2 crystal was removed by I2 in acetone. Pieces of the resultantβ-Fe4Se5 crystal-like sheets were finally obtained by repeated cleaving usingthe Scotch-tape method.

Fig. 5. Possible Fe-vacancy orders in β-Fe1-xSe and their corresponding stoichiometry. (A) x = 0.5; (B) x = 0.333; (C–E) x = 0.25; (F) x = 0.2; (G and H) x = 0.167;(I) x = 0.143; (J and K) x = 0.125; and (L) x = 0.1. Se atoms were hidden for better visibility. Solid and open circles denote Fe atoms and Fe vacancies, re-spectively. Green area encloses the original β-FeSe unit cell. Black lines connect nearest Fe vacancies to improve the visibility of the order pattern.

Fig. 6. Sketch of the proposed temperature-doping phase diagram of Fe-Sesuperconducting system, showing regions for antiferromagnetism (AFM)and superconductivity (SC).

Chen et al. PNAS | January 7, 2014 | vol. 111 | no. 1 | 67

PHYS

ICS

Nanosheets. Se nanoparticles were synthesized before the formation ofFeSe nanosheets. Eighty milliliters of ethylene glycol was added into a three-neck flask equipped with a standard Schlenk line, together with poly-vinylpyrrolidone (PVP, molecular weight = 40000), NaOH, and SeO2 powderwith a ratio of 1:3:1.66 (in molar ratio). The mixture was then heated to 160 °C,followed by addition of 2.4 mL of hydrazine hydrate as a reducing agent.The Fe precursor solution was made by dissolving 2.3857 g of FeCl2 in 20 mLethylene glycol. It was then injected into the above mixture at 160 °C andheld for 12 h for the formation of FeSe nanosheets. To dry the products, wefirst removed the capping ligands on the FeSe nanosheets by dispersing inacetone with diluted ethanol (10% vol/vol) and stirring until they wereprecipitated. The supernatant was decanted, and the precipitates werewashed three times with acetone to remove the residual PVP. The nano-sheets were finally collected by centrifugation and dried in vacuum.

Nanowires. FeSe nanowires were grown via a two-step process, called the on-film formation of nanowires (OFF-ON) method (41). FeSe thin films were firstdeposited (42) and then annealed at 400 °C for 120 h in vacuum.

Structure Characterization. TEM samples of FeSe crystals and sheets weremade by smashing a small piece of cleaved crystal immersed in ethanol ina mortar and then collecting it using Lacey carbon grids. FeSe nanosheets

were suspended in ethanol and collected by Lacey carbon grids. Samples ofFeSe crystals were analyzed by a JEOL 3000F microscope equipped with anINCA EDX system. Samples of FeSe nanosheets and nanowires were analyzedby a JEOL 2100F microscope equipped with an OXFORD X-Max EDX analyzer.Lattice constants were calculated from interplanar spacings in the SAEDpatterns and refined by a nonlinear least-squares cell refinement program(43). Simulations of electron diffractions were carried out by MacTempas(www.totalresolution.com/MacTempasX.htm).

Physical Property Measurements. The resistances of small pieces of FeSe sheetsand FeSe nanowires were measured with a Physical Property MeasurementSystem (PPMS) (Quantum Design) using the four-point and two-point methods,respectively. The magnetic properties were measured on a SuperconductingQuantum Interference Device (SQUID) magnetometer [Magnetic PropertyMeasurement System (MPMS); Quantum Design].

ACKNOWLEDGMENTS. We thank Dr. Phillip Wu for valuable suggestions andDr. T. K. Lee for fruitful discussions. Technical support from NanoCore, the CoreFacilities for Nanoscience and Nanotechnology at Academia Sinica in Taiwan, isacknowledged. This work was supported by the National Science Council, theAcademia Sinica of Taiwan, and the US Air Force Office of Scientific Research/Asian Office of Aerospace Research and Development (AFOSR/AOARD).

1. Hsu FC, et al. (2008) Superconductivity in the PbO-type structure alpha-FeSe. Proc NatlAcad Sci USA 105(38):14262–14264.

2. McQueen TM, et al. (2009) Extreme sensitivity of superconductivity to stoichiometry inFe1+delta Se. Phys Rev B 79(1):014522.

3. Okamoto H (1991) The Fe-Se (iron-selenium) system. J Phase Equilibria 12(3):383.4. Pomjakushina E, Conder K, Pomjakushin V, Bendele M, Khasanov R (2009) Synthesis,

crystal structure, and chemical stability of the superconductor FeSe1-x. Phys Rev B80(2):024517.

5. McQueen TM, et al. (2009) Tetragonal-to-orthorhombic structural phase transition at90 K in the superconductor Fe(1.01)Se. Phys Rev Lett 103(5):057002.

6. Liu TJ, et al. (2010) From (π,0) magnetic order to superconductivity with (π,π) magneticresonance in Fe(1.02)Te(1-x)Se(x). Nat Mater 9(9):716–720.

7. Paglione J, Greene RL (2010) High-temperature superconductivity in iron-based ma-terials. Nat Phys 6(9):645–658.

8. Ying TP, et al. (2012) Observation of superconductivity at 30∼46 K in A(x)Fe₂Se₂(A = Li,Na, Ba, Sr, Ca, Yb, and Eu). Sci Rep 2:426.

9. Ye F, et al. (2011) Common crystalline and magnetic structure of superconductingA2Fe4Se5 (A=K,Rb,Cs,Tl) single crystals measured using neutron diffraction. Phys RevLett 107(13):137003.

10. Wang Z, et al. (2011) Microstructure and ordering of iron vacancies in the super-conductor system K_{y}Fe_{x}Se_{2} as seen via transmission electron microscopy. PhysRev B 83(14):140505.

11. Li W, et al. (2012) Phase separation and magnetic order in K-doped iron selenidesuperconductor. Nat Phys 8(2):126–130.

12. Wang Z-W, et al. (2012) Structural phase separation in K0.8Fe1.6+xSe2 super-conductors. J Phys Chem C 116(33):17847–17852.

13. Yan YJ, et al. (2012) Electronic and magnetic phase diagram in K(x)Fe(2-y)Se(2) su-perconductors. Sci Rep 2:212.

14. Li W, et al. (2012) KFe2Se2 is the parent compound of K-doped iron selenide super-conductors. Phys Rev Lett 109(5):057003.

15. Yuan RH, et al. (2012) Nanoscale phase separation of antiferromagnetic order andsuperconductivity in K(0.75)Fe(1.75)Se(2). Sci Rep 2:221.

16. Fang M-H, et al. (2011) Fe-based superconductivity with Tc=31 K bordering an anti-ferromagnetic insulator in (Tl,K)FexSe2. EPL 94(2):27009.

17. Song YJ, et al. (2011) Phase transition, superstructure and physical properties ofK2Fe4Se5. EPL 95(3):37007.

18. Kazakov SM, et al. (2011) Uniform patterns of Fe-vacancy ordering in the Kx(Fe,Co)2–ySe2 superconductors. Chem Mater 23(19):4311–4316.

19. Ding X, et al. (2013) Influence of microstructure on superconductivity in KxFe₂-ySe₂and evidence for a new parent phase K₂Fe₇Se₈. Nat Commun 4:1897.

20. Zhang A-m, et al. (2013) Superconductivity at 44 K in K intercalated FeSe system withexcess Fe. Sci Rep 3:1216.

21. Mizuguchi Y, Tomioka F, Tsuda S, Yamaguchi T, Takano Y (2008) Superconductivity at27 K in tetragonal FeSe under high pressure. Appl Phys Lett 93(15):152505.

22. Medvedev S, et al. (2009) Electronic and magnetic phase diagram of beta-Fe(1.01)Sewith superconductivity at 36.7 K under pressure. Nat Mater 8(8):630–633.

23. Margadonna S, et al. (2009) Pressure evolution of the low-temperature crystalstructure and bonding of the superconductor FeSe (T[sub c] = 37 K). Phys Rev B 80(6):064506.

24. Wang QY, et al. (2012) Interface-induced high-temperature superconductivity insingle unit-cell FeSe films on SrTiO3. Chin Phys Lett 29(3):037402.

25. Liu D, et al. (2012) Electronic origin of high-temperature superconductivity in single-layer FeSe superconductor. Nat Commun 3:931.

26. He S, et al. (2013) Phase diagram and electronic indication of high-temperature su-perconductivity at 65 K in single-layer FeSe films. Nat Mater 12(7):605–610.

27. Chang C-C, et al. (2012) Superconductivity in PbO-type tetragonal FeSe nanoparticles.Solid State Commun 152(8):649–652.

28. Wu M-K, Wang M-J, Yeh K-W (2013) Recent advances in β -FeSe1−x and related su-perconductors. Sci Technol Adv Mater 14(1):014402.

29. Shoemaker DP, et al. (2012) Phase relations in K_{x}Fe_{2−y}Se_{2} and the structureof superconducting K_{x}Fe_{2}Se_{2} via high-resolution synchrotron diffraction.Phys Rev B 86(18):184511.

30. Chen CH, Cheong SW (1996) Commensurate to incommensurate charge ordering andits real space images in La0.5Ca0.5MnO3. Phys Rev Lett 76(21):4042–4045.

31. Yan X-W, Gao M, Lu Z-Y, Xiang T (2011) Electronic structures and magnetic order ofordered-Fe-vacancy ternary iron selenides TlFe1.5Se2 and AFe1.5Se2 (A=K, Rb, or Cs).Phys Rev Lett 106(8):087005.

32. Song C-L, et al. (2011) Direct observation of nodes and twofold symmetry in FeSesuperconductor. Science 332(6036):1410–1413.

33. Wells BO, et al. (1997) Incommensurate spin fluctuations in high-transition temper-ature superconductors. Science 277(5329):1067–1071.

34. Lumsden MD, et al. (2010) Evolution of spin excitations into the superconductingstate in FeTe1-xSex. Nat Phys 6(3):182–186.

35. Xia Y, et al. (2009) Fermi surface topology and low-lying quasiparticle dynamics ofparent Fe1+xTe/Se superconductor. Phys Rev Lett 103(3):037002.

36. Hisashi K, Masaki F (2012) Magnetic excitations in iron chalcogenide superconductors.Sci Technol Adv Mater 13(5):054302.

37. Han F, et al. (2012) Metastable superconducting state in quenched KxFe2−ySe2. PhilosMag 92(19-21):2553–2562.

38. Ryu H, Lei H, Frenkel AI, Petrovic C (2012) Local structural disorder and supercon-ductivity in K_{x}Fe_{2-y}Se_{2}. Phys Rev B 85(22):224515.

39. Berlijn T, Hirschfeld PJ, Ku W (2012) Effective doping and suppression of Fermi surfacereconstruction via Fe vacancy disorder in K(x)Fe(2-y)Se2. Phys Rev Lett 109(14):147003.

40. Wang AF, et al. (2011) Superconductivity at 32 K in single-crystalline Rb_{x}Fe_{2-y}Se_{2}. Phys Rev B 83(6):060512.

41. Ham J, et al. (2009) Direct growth of compound semiconductor nanowires by on-filmformation of nanowires: Bismuth telluride. Nano Lett 9(8):2867–2872.

42. Wang MJ, et al. (2009) Crystal orientation and thickness dependence of the super-conducting transition temperature of tetragonal FeSe1-x thin films. Phys Rev Lett103(11):117002.

43. Holland TJB, Redfern SAT (1997) Unit cell refinement from powder diffraction data:The use of regression diagnostics. Mineralogical Magazine 61:65–77.

68 | www.pnas.org/cgi/doi/10.1073/pnas.1321160111 Chen et al.